5,135 research outputs found

    Remarks on topological models and fractional statistics

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    One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tensor gauge field, namely BF model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of string interaction. A dimensional reduction of the previous model provides a (2+1) dimensional topological theory, which involves a 2-form B and a 0-form Ď•\phi. Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in others space-time dimensions, and in particular to the case of strings in four dimensions. In this context, discussions about fractional spin and antisymmetric tensor field are presented

    Three-dimensional fractional-spin gravity

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    Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal non-abelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(N,N +/- 1) or gl(N|N +/- 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell.Comment: 38 pages, 2 tables. References [7,13,61] added with comments in the second version. To appear in JHE

    A note on the topological order of noncommutative Hall fluids

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    We evaluate the ground state degeneracy of noncommutative Chern-Simons models on the two-torus, a quantity that is interpreted as the "topological order" of associated phases of Hall fluids. We define the noncommutative theory via T-duality from an ordinary Chern-Simons model with non-abelian 't Hooft magnetic fluxes. Motivated by this T-duality, we propose a discrete family of noncommutative, non-abelian fluid models, arising as a natural generalization of the standard noncommutative Chern-Simons effective models. We compute the topological order for these universality classes, and comment on their possible microscopic interpretation.Comment: 14 page

    Particle Physics and Condensed Matter: The Saga Continues

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    Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the abundance of results reported at the Nobel Symposium on "New Forms of Matter, Topological Insulators and Superconductors". Since they distill some most basic ideas in their simplest forms, these concluding remarks might also serve, for non-specialists, as an introduction.Comment: 18 pages, 3 figures. Invited presentation of concluding remarks at Nobel Symposium 156 on New Forms of Matter, Topological Insulators and Superconductors, June 13-15 2014, H\"ogberga G{\aa}rd, Stockhol

    Remarks on Charged Vortices in the Maxwell-Chern-Simons Model

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    We study vortex-like configuration in Maxwell-Chern-Simons Electrodynamics. Attention is paid to the similarity it shares with the Nielsen-Olesen solutions at large distances. A magnetic symmetry between a point-like and an azimuthal-like current in this framework is also pointed out. Furthermore, we address the issue of a neutral and spinless particle interacting with a charged vortex, and obtain that the Aharonov-Casher-type phase depends upon mass and distance parameters.Comment: New refs. added. Version accepted for publication in Phys. Lett.

    Topological and symmetry broken phases of Z_N parafermions in one dimension

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    We classify the gapped phases of Z_N parafermions in one dimension and construct a representative of each phase. Even in the absence of additional symmetries besides parafermionic parity, parafermions may be realized in a variety of phases, one for each divisor n of N. The phases can be characterized by spontaneous symmetry breaking, topology, or a mixture of the two. Purely topological phases arise if n is a unitary divisor, i.e. if n and N/n are co-prime. Our analysis is based on the explicit realization of all symmetry broken gapped phases in the dual Z_N-invariant quantum spin chains.Comment: 16 pages; v2: improved exposition and additional reference
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